Importance: Medium ✭✭
Author(s): Samal, Robert
Subject: Graph Theory
» Coloring
» » Homomorphisms
Keywords: Cayley graph
Recomm. for undergrads: no
Posted by: Robert Samal
on: March 6th, 2007
Conjecture   Let $ M $ be an abelian group. Is the core of a Cayley graph (on some power of $ M $) a Cayley graph (on some power of $ M $)?

Even the case $ M=\mathbb{Z}_2 $ is open. In this case, Cayley graphs on some power of $ \mathbb{Z}_2 $ are called cube-like graphs, they have been introduced by Lov\'asz as an example of graphs, for which every eigenvalue is an integer.

So, in this case we ask, whether a core of each cube-like graph is a cube-like graph.


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